I've installed, configured, have a test event, ticket, booking setup but when entering the booking form and clicking "Send your booking" I am re-directed to the same page, with the default message "No Event".

I confirmed by installing to a bare bones WP and see what you're saying... the inline response and insert worked fine.

I've disabled each plugin individually and then all plugins with no luck, so I guess my theme is the culprit. I really don't want to try switching themes, I spent a good deal of time configuring menu's and widgets.

Are there known themes or JS that cause issues? Is there a traditional post and return version of Event Manager?

is it possible to change to default theme temporarily so that we can determine if its really your theme and deactivating other plugins temporarily. OR just change your theme and let your other plugins active.